I can't even tell the difference between a lot of 8 bit colors... Why make them 16 bit? (We're talking about going from 2^24 different hues to 2^48 different hues, right? And going from 2^8 different amounts of transparency to 2^16 different amounts of transparency, right?)
When you are doing adjustments you need the extra color space/precision. This is a significant reason why most photographers will shoot in RAW mode rather than using the fast in-camera JPG conversion; once you go to JPG you've lost a great deal of the photographic information so lose the chance to adjust exposure, white balance, and contrast to bring out details of the image. As you make those adjustments, even if you start with an 8-bit image, the 16 bits of precision allow you to make multiple such adjustments in series without unwanted side effects (banding, detail loss, etc).
Imagine a calculator that doesn't keep anything after the decimal point, and using that to do algebra homework. Lack of precision is a significant handicap.
Working in 16 bits (or more) is a requirement for any photo manipulation prior to the output photo stage. PSE and Pixelmator being 8-bit meant that they always had to be the very last step in any photo touch-up workflow, which meant that a lot of the fancy tools they brought to bear were useless.